See, this is a great example of why people who don't understand basic electronic theory shouldn't putz around with electronics.
First, let's cover the alternator. Even at maximum factory load, you've got plenty of headroom with your stock alternator. Unless your "few lights" are a couple Twinsonics on the roof, you're fine here. To give you an idea, my F150 has a 150A alternator as well (hell, maybe the exact same alternator you've got) and I can almost guarantee that my sustained electrical load is substantially higher than yours. No problem.
Second, the capacitor. Caps, as used in vehicle electrical systems, are designed to provide some extra power on demand (usually, when the subwoofer hits). They also "smooth" the total power draw from the vehicle's electrical system. They also add NO capacity (beyond a few milliseconds) to the system.
You've convoluted so many things in this thread that it's difficult to tell what your problem really is. I'm going to assume that the real issue is that you want to leave your lights running while on scene, but not idle the vehicle, presumably to save gas. Is this a correct assumption? Validate this assumption, then I'll provide some more information.